Given a sorted array of N+2 integers between 0 and N with exactly one duplicate, design a logarithmic time algorithm to find the duplicate. Note: you don't need to write a code. Just use your English words to describe the algorithm
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- A square matrix can be represented by a two-dimensional array with N rows and N columns. You may assume a maximum size of 50 rows and 50 columns. 1. Write an algorithm MakeEmpty(n), which sets the first n rows and n columns to zero.2. Write an algorithm Add(M1, M2, M3), which adds two matrices M1 and M2 together to produce matrix M3.3. Write an algorithm Subtract(M1, M2, M3), which subtracts matrix M2 from matrix M1 to produce matrix M3.4. Write an algorithm Copy(M1, M2), which copies matrix M1 into matrix M2. Answer 3 and 4 AlgorithmsA square matrix can be represented by a two-dimensional array with N rows and N columns. You may assume a maximum size of 50 rows and 50 columns. 1. Write an algorithm MakeEmpty(n), which sets the first n rows and n columns to zero.2. Write an algorithm Add(M1, M2, M3), which adds two matrices M1 and M2 together to produce matrix M3.3. Write an algorithm Subtract(M1, M2, M3), which subtracts matrix M2 from matrix M1 to produce matrix M3.4. Write an algorithm Copy(M1, M2), which copies matrix M1 into matrix M2. Answer 1 and 2 questions with codeYou are given two different methods for sorting the values in an array: Sort1 and Sort2. You have determined that Sort1 = O(nlog n) and Sort2 = O(n2). You need to choose one of these two sorting methods to sort lists in a program you are writing, but you would like to choose the one which completes the fastest. Given this information, is either of these two methods guaranteed to be complete faster than the other? If so, explain which one is faster and why. If not, explain why not.
- # Exercise 1. Implement the algorithm covered in lectures that determines if an integer n is prime. Your function should return True, if n is prime, and False otherwise. Your algorithm has to be effective for n ~ 1,000,000,000,000.def isPrime(n):You are asked to sort n English words alphabetically. What is the best achievable complexity? (Note: we are talking about actual English words that can be found in a Marriam-Webster dictionary.) Describe the algorithm that achieves the best complexity.I need the code from start to end with no errors and the explanation for the code ObjectivesJava refresher (including file I/O)Use recursionDescriptionFor this project, you get to write a maze solver. A maze is a two dimensional array of chars. Walls are represented as '#'s and ' ' are empty squares. The maze entrance is always in the first row, second column (and will always be an empty square). There will be zero or more exits along the outside perimeter. To be considered an exit, it must be reachable from the entrance. The entrance is not an exit.Here are some example mazes:mazeA7 9# # ###### # # ## # # #### # ## ##### ## ########## RequirementsWrite a MazeSolver class in Java. This program needs to prompt the user for a maze filename and then explore the maze. Display how many exits were found and the positions (not indices) of the valid exits. Your program can display the valid exits found in any order. See the examples below for exact output requirements. Also, record…
- For the following problem please write an algorithm in plain English .i.e give details as to how you will solve the problem.A deck of 52 playing cards (as used for playing bridge) has to be sorted. At the end of the attempt, the sorted deck of cards should be on the table with the backside up.The order within a suite is Ace - King - Queen - Jack- 10 -9 - 8 - 7- 6- 5- 4- 3- 2. The very first card in the sorted deck is the Ace of Clubs, the next ones are the King of Clubs, the Queen of Clubs, the Jack of Clubs, the 10 of Clubs ... down to the 2 of Clubs. The next card is Ace of Spades, followed by the King of Spades etc. The hearts and diamonds cards follow in the same order.The deck of cards must be well-shuffled immediately prior to the challenge.Please write the algorithm in steps like you write a recipe for a dish.If any steps need to be repeated try to use a loop.Please try to not use any programming language.(IT's one question just with a lot of instructions to be understood well)Mina always wants things to be sorted. She loves perfection in work and doesn't worry about time. Her brother gifted her some boxes with different sizes. Now she needs your help to sort it. You're given n boxes with different sizes and your task is to sort the boxes in ascending order of size. You should recursively partition the array with a number p so that all the elements greater than p are to its right and all the elements lower than p to its left to sort the boxes. Make sure you are giving a solution that doesn't exceed the time complexity of O(n^2), but on average has complexity of O(nlogn) a. Which algorithm will you suggest to Mina? Explain if your algorithm is stable or unstable with appropriate example b. Show the step by step simulation of your algorithm on the boxes of size 5, 9, 10, 3, 15, 12, 6, 20, 9, 13, 3, 10, 1, 2. c. Give an example of box sizes when it will be worst case and when it will be the best case for this algorithm.The solution must be recursive. inputAndPrintReverse:Inputs integers from the user until the user enters 0, then prints the integers in reverse order. For this method, you may NOT use an array or any type of array structure, in other words, you may not use any structure to store the user input.
- Calculating the Minimum Sum Path in a Triangle (LeetCode Problem)Given a triangle array, return the minimum path sum from top to bottom. For each step, you may move toan adjacent number of the row below. More formally, if you are on index i on the current row, you maymove to either index i or index i + 1 on the next row. public static int minSumPathMemo(int[][] triangle)This method will calculate the minimum sum path in the triangle using the top down strategy. Note thismethod MUST BE recursive and you will need to create a recursive helper method. public static int minSumPathBottomUp(int[][] triangle)This method will calculate the minimum sum path in the triangle using the bottom up strategy. Note thismethod CANNOT be recursive and you should not create any additional helper functions. Extra Challenge: Could you do this using only O(n) extra space where n is the total number of rows in thetriangle? This is method signature class below: package dynamic; public class MinSumPath {…You have an array of 10,000 subject scores for a high-school exam and you want to find the scores that are ranked from 4900 to 5100 that is the 201 most middle-ranked scores. Precisely describe two alternative algorithmic ap proaches to doing this - one of which is, in terms of time complexity, more efficient than the other.The Fibonacci algorithm is a famous mathematical function that allows us to create a sequence of numbers by adding together the two previous values. For example, we have the sequence:1, 1, 2, 3, 5, 8, 13, 21…Write your own recursive code to calculate the nth term in the sequence. You should accept a positive integer as an input, and output the nth term of the sequence.Once you have created your code, add comments describing how the code works, and the complexity of any code you have created.